[機統] Law of Large Number
X_i: i.i.d
C_i: i.i.d and C_i = ±1/n with equal probability
X_i, C_i are independent
Prove that S_n converges to a deterministic value in mean-square sense (L^2)
and in almost sure sense
(or disprove)
n
(1) S_n = Σ X_i C_i
i=1
n
(2) S_n = (1/n) Σ X_i X_{i+1}
i=1
n
(3) S_n = Σ X_i X_{i+1} C_i
i=1
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